One strategy that the administration weighed last summer was to leave a tiny residual force, perhaps as few as 3,000 troops — not enough to secure the country, just enough to make a tempting and vulnerable target. Another would be to stay on uninvited. With a majority of Iraqis already seeing the United States as an occupier not a liberator, that would have been a bonanza for the Iranians and Islamist radicals alike.